Project Grant 2506431
- This $200,000 four-year project grant was awarded by the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) to North Carolina State University to conduct research in geometric topology, including the study of knots, three- and four-dimensional shapes, and the development of tools to measure the complexity of these objects. The project aims to produce new exotic smooth four-manifolds, study surfaces in four-manifolds, and apply instanton gauge theory to address...
- This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides funding of $226,665 to the University of Virginia (UVA) for research focused on the geometric classification and topological properties of 4-dimensional manifolds. The objectives include examining the validity of 4-dimensional topological surgery theory, studying symmetries of 4-dimensional spaces, and developing new tools for distinguishing them. The project...
- This Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research into the topology and dynamics of four-dimensional manifolds with symplectic structures. The $156,571 award, spanning from September 1, 2024 to August 31, 2026, will enable the principal investigator to employ advanced mathematical tools, such as surgery on Lefschetz fibrations, Gromov-Witten theory, and family...
- This Project Grant award of $150,000 from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research at the University of Chicago to develop a theory of mapping class groups of closed 4-dimensional manifolds. The goal is to understand fundamental relationships between symmetries arising in different areas of mathematics, such as the connections between certain 4-dimensional spaces central in physics and collections of reflective symmetries of...
- This Project Grant award of $317,407 from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support research at the University of Nebraska on the topology of 3- and 4-dimensional manifolds. The project aims to uncover deep connections between manifold theory in these dimensions, with potential applications in fields such as biology, chemistry, physics, and quantum computing. Specific objectives include proving additional cases of the Smooth...
- This $260,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on geometric limits in low dimensional geometry and topology at Boston College. The key objectives of the project are to analyze the global topology of the "space of all hyperbolic manifolds" and study the relationship between the "rank" of closed hyperbolic 3-manifolds and their geometry. In addition to the research...
- This $204,372 federal Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports research on the potential theoretic aspects of complex geometry. The principal investigator will employ methods from potential theory, infinite-dimensional geometry, and geometric analysis to investigate a cluster of interconnected questions and conjectures in complex geometry. The project aims to advance scientific knowledge in this...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $170,443 Project Grant to the University of Massachusetts Boston (UMass Boston) under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research in "Critical Symplectic Geometry, Lagrangian Cobordisms, and Stable Homotopy Theory." The project aims to incorporate ideas from homotopy theory and category theory into symplectic geometry to prove structural results about...
- This National Science Foundation Project Grant of $250,000 supports research into low-dimensional topology through July 2025. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), the award to Duke University will advance understanding of fundamental questions in knot theory and 4-manifold topology. Specifically, the principal investigator will investigate knot concordance problems tied to the unique properties of 4-dimensional manifolds compared to higher dimensions....
- The National Science Foundation Division of Mathematical Sciences awarded a $389,346 Project Grant to the Georgia TECH Research Corporation for research titled "Topology Between Dimensions Three and Four." The award period is from June 1, 2021 through May 31, 2024. The grant is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these fields and strengthen the nation's scientific enterprise through increasing knowledge and...
This $100,000 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) aims to develop a deeper understanding of the topology and geometry of four-dimensional spaces. The research will explore similarities and differences among these spaces when equipped with additional geometric structures, such as smooth, symplectic, and complex structures, using a mix of mathematical methods. Key goals include constructing exotic smooth structures on 4-manifolds, developing new examples of 4-manifolds with definite or signature-zero intersection forms, and producing symplectic analogues of complex surfaces. The project also investigates smooth mapping class groups and equivariant embeddings of surfaces in the 4-sphere, utilizing techniques from gauge theory, geometric group theory, and symplectic/contact topology. The award supports research opportunities for graduate and undergraduate students, and broader community contributions through workshops and summer schools.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $100.0k | 8/5/25 |